(x-1)(x-3)=(x-2)(x+3)

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Solution for (x-1)(x-3)=(x-2)(x+3) equation:


Simplifying
(x + -1)(x + -3) = (x + -2)(x + 3)

Reorder the terms:
(-1 + x)(x + -3) = (x + -2)(x + 3)

Reorder the terms:
(-1 + x)(-3 + x) = (x + -2)(x + 3)

Multiply (-1 + x) * (-3 + x)
(-1(-3 + x) + x(-3 + x)) = (x + -2)(x + 3)
((-3 * -1 + x * -1) + x(-3 + x)) = (x + -2)(x + 3)
((3 + -1x) + x(-3 + x)) = (x + -2)(x + 3)
(3 + -1x + (-3 * x + x * x)) = (x + -2)(x + 3)
(3 + -1x + (-3x + x2)) = (x + -2)(x + 3)

Combine like terms: -1x + -3x = -4x
(3 + -4x + x2) = (x + -2)(x + 3)

Reorder the terms:
3 + -4x + x2 = (-2 + x)(x + 3)

Reorder the terms:
3 + -4x + x2 = (-2 + x)(3 + x)

Multiply (-2 + x) * (3 + x)
3 + -4x + x2 = (-2(3 + x) + x(3 + x))
3 + -4x + x2 = ((3 * -2 + x * -2) + x(3 + x))
3 + -4x + x2 = ((-6 + -2x) + x(3 + x))
3 + -4x + x2 = (-6 + -2x + (3 * x + x * x))
3 + -4x + x2 = (-6 + -2x + (3x + x2))

Combine like terms: -2x + 3x = 1x
3 + -4x + x2 = (-6 + 1x + x2)

Add '-1x2' to each side of the equation.
3 + -4x + x2 + -1x2 = -6 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x + 0 = -6 + 1x + x2 + -1x2
3 + -4x = -6 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -4x = -6 + 1x + 0
3 + -4x = -6 + 1x

Solving
3 + -4x = -6 + 1x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.
3 + -4x + -1x = -6 + 1x + -1x

Combine like terms: -4x + -1x = -5x
3 + -5x = -6 + 1x + -1x

Combine like terms: 1x + -1x = 0
3 + -5x = -6 + 0
3 + -5x = -6

Add '-3' to each side of the equation.
3 + -3 + -5x = -6 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = -6 + -3
-5x = -6 + -3

Combine like terms: -6 + -3 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8

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